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 October 26th, 2007, 08:54 PM #1 Newbie   Joined: Oct 2007 Posts: 4 Thanks: 0 Conditional Expectation and Variance Question Here's the question I'm having trouble with: Show Var[E[Y|X]] = 0 given random variables X and Y are independent, keeping in mind Var[Y] = Var[E[Y|X]] + E[Var[Y|X]]. Here's the work I've done so far. 1) Var[E[Y|X]] = E[(E[Y|X])^2] - (E[E[Y|X]])^2 (using Var[X] = E[X^2] - (E[X])^2) 2) Var[E[Y|X]] = E[E[Y|X]^2] - (E[Y])^2 (using E[Y|X] = E[Y] if X, Y are independent) 3) E[Y]^2 - E[Y]^2 (I want to use E[Y] = E[E[Y|X]] and but I need E[E[Y|X]^2] = E[E[Y|X]]^2 What am I missing here? Thanks in advance. October 30th, 2007, 12:05 PM #2 Member   Joined: Nov 2006 From: Vancouver, Canada Posts: 46 Thanks: 0 Hmm.. That's a silly question your prof gave. I mean E(Y|X) = E(Y) due to independence, and so E(Y) is just a single number, of course Var(E(Y)) is 0... Did I understand the question wrong? Tags conditional, expectation, question, variance Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post lebesguedd Algebra 0 November 19th, 2013 04:36 AM Juliayaho Algebra 0 October 1st, 2012 06:34 PM blabla Advanced Statistics 2 April 11th, 2012 11:48 AM hendaz Algebra 2 May 23rd, 2010 01:57 PM hendaz Advanced Statistics 1 May 18th, 2010 01:13 PM

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